Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Impact of mutant beta-catenin on ABCB1 expression and therapy response in colon cancer cells

Background: Colorectal cancers are often chemoresistant toward antitumour drugs that are substrates for ABCB1-mediated multidrug resistance (MDR). Activation of the Wnt/beta-catenin pathway is frequently observed in colorectal cancers. This study investigates the impact of activated, gain-of-function beta-catenin on the chemoresistant phenotype. Methods: The effect of mutant (mut) beta-catenin on ABCB1 expression and promoter activity was examined using HCT116 human colon cancer cells and isogenic sublines harbouring gain-of-function or wild-type beta-catenin, and patients' tumours. Chemosensitivity towards 24 anticancer drugs was determined by high throughput screening. Results: Cell lines with mut beta-catenin showed high ABCB1 promoter activity and expression. Transfection and siRNA studies demonstrated a dominant role for the mutant allele in activating ABCB1 expression. Patients' primary colon cancer tumours shown to express the same mut beta-catenin allele also expressed high ABCB1 levels. However, cell line chemosensitivities towards 24 MDR-related and non-related antitumour drugs did not differ despite different beta-catenin genotypes. Conclusion: Although ABCB1 is dominantly regulated by mut beta-catenin, this did not lead to drug resistance in the isogenic cell line model studied. In patient samples, the same beta-catenin mutation was detected. The functional significance of the mutation for predicting patients' therapy response or for individualisation of chemotherapy regimens remains to be established

A Centre-Stable Manifold for the Focussing Cubic NLS in R1+3R^{1+3}

Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$i\psi_t+\Delta\psi = -|\psi|^2 \psi.$$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$) solution of $$-\Delta \phi + \alpha\phi = \phi^3.$$ The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form $e^{i(v \cdot + \Gamma)} \phi(\cdot - y, \alpha)$. We prove that any solution starting sufficiently close to a standing wave in the $\Sigma = W^{1, 2}(R^3) \cap |x|^{-1}L^2(R^3)$ norm and situated on a certain codimension-one local Lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves. Furthermore, we show that \mc N is invariant under the Hamiltonian flow, locally in time, and is a centre-stable manifold in the sense of Bates, Jones. The proof is based on the modulation method introduced by Soffer and Weinstein for the $L^2$-subcritical case and adapted by Schlag to the $L^2$-supercritical case. An important part of the proof is the Keel-Tao endpoint Strichartz estimate in $R^3$ for the nonselfadjoint Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page

Evolution of the complex refractive index in the UV spectral region in ageing secondary organic aerosol

The chemical and physical properties of secondary organic aerosol (SOA) formed by the photochemical degradation of biogenic and anthropogenic volatile organic compounds (VOC) are as yet still poorly constrained. The evolution of the complex refractive index (RI) of SOA, formed from purely biogenic VOC and mixtures of biogenic and anthropogenic VOC, was studied over a diurnal cycle in the SAPHIR photochemical outdoor chamber in Jülich, Germany. The correlation of RI with SOA chemical and physical properties such as oxidation level and volatility was examined. The RI was retrieved by a newly developed broadband cavity-enhanced spectrometer for aerosol optical extinction measurements in the UV spectral region (360 to 420 nm). Chemical composition and volatility of the particles were monitored by a high-resolution time-of-flight aerosol mass spectrometer, and a volatility tandem differential mobility analyzer. SOA was formed by ozonolysis of either (i) a mixture of biogenic VOC (α-pinene and limonene), (ii) biogenic VOC mixture with subsequent addition of an anthropogenic VOC (<i>p</i>-xylene-d₁₀), or (iii) a mixture of biogenic and anthropogenic VOC. The SOA aged by ozone/OH reactions up to 29.5 h was found to be non-absorbing in all cases. The SOA with <i>p</i>-xylene-d₁₀ showed an increase of the scattering component of the RI correlated with an increase of the O / C ratio and with an increase in the SOA density. There was a greater increase in the scattering component of the RI when the SOA was produced from the mixture of biogenic VOCs and anthropogenic VOC than from the sequential addition of the VOCs after approximately the same ageing time. The increase of the scattering component was inversely correlated with the SOA volatility. Two RI retrievals determined for the pure biogenic SOA showed a constant RI for up to 5 h of ageing. Mass spectral characterization shows the three types of the SOA formed in this study have a significant amount of semivolatile components. The influence of anthropogenic VOCs on the oxygenated organic aerosol as well as the atmospheric implications are discussed

Surgical therapy of celiac axis and superior mesenteric artery syndrome

INTRODUCTION Compression syndromes of the celiac artery (CAS) or superior mesenteric artery (SMAS) are rare conditions that are difficult to diagnose; optimal treatment remains complex, and symptoms often persist after surgery. We aim to review the literature on surgical treatment and postoperative outcome in CAS and SMAS syndrome. METHODS A systematic literature review of medical literature databases on the surgical treatment of CAS and SMAS syndrome was performed from 2000 to 2022. Articles were included according to PROSPERO guidelines. The primary endpoint was the failure-to-treat rate, defined as persistence of symptoms at first follow-up. RESULTS Twenty-three studies on CAS (n = 548) and 11 on SMAS (n = 168) undergoing surgery were included. Failure-to-treat rate was 28% for CAS and 21% for SMAS. Intraoperative blood loss was 95 ml (0-217) and 31 ml (21-50), respectively, and conversion rate was 4% in CAS patients and 0% for SMAS. Major postoperative morbidity was 2% for each group, and mortality was described in 0% of CAS and 0.4% of SMAS patients. Median length of stay was 3 days (1-12) for CAS and 5 days (1-10) for SMAS patients. Consequently, 47% of CAS and 5% of SMAS patients underwent subsequent interventions for persisting symptoms. CONCLUSION Failure of surgical treatment was observed in up to every forth patient with a high rate of subsequent interventions. A thorough preoperative work-up with a careful patient selection is of paramount importance. Nevertheless, the surgical procedure was associated with a beneficial risk profile and can be performed minimally invasive

Structural models of genome-wide covariance identify multiple common dimensions in autism

Common genetic variation has been associated with multiple symptoms in Autism Spectrum Disorder (ASD). However, our knowledge of shared genetic factor structures contributing to this highly heterogeneous neurodevelopmental condition is limited. Here, we developed a structural equation modelling framework to directly model genome-wide covariance across core and non-core ASD phenotypes, studying autistic individuals of European descent using a case-only design. We identified three independent genetic factors most strongly linked to language/cognition, behaviour and motor development, respectively, when studying a population-representative sample (N=5,331). These analyses revealed novel associations. For example, developmental delay in acquiring personal-social skills was inversely related to language, while developmental motor delay was linked to self-injurious behaviour. We largely confirmed the three-factorial structure in independent ASD-simplex families (N=1,946), but uncovered simplex-specific genetic overlap between behaviour and language phenotypes. Thus, the common genetic architecture in ASD is multi-dimensional and contributes, in combination with ascertainment-specific patterns, to phenotypic heterogeneity

Biases in the perceived timing of perisaccadic perceptual and motor events

Subjects typically experience the temporal interval immediately following a saccade as longer than a comparable control interval. One explanation of this effect is that the brain antedates the perceptual onset of a saccade target to around the time of saccade initiation. This could explain the apparent continuity of visual perception across eye movements. Thisantedating account was tested in three experiments in which subjects made saccades of differing extents and then judged either the duration or the temporal order of key events. Postsaccadic stimuli underwent subjective temporal lengthening and had early perceived onsets. A temporally advanced awareness of saccade completion was also found, independently of antedating effects. These results provide convergent evidence supporting antedating and differentiating it from other temporal biases